External validation, recalibration, and clinical utility of the prognostic model kidney failure risk equation in patients with CKD stages G3-4: a nationwide retrospective cohort analysis in Peru

Main Analysis - Winsorization 1.5%: 4. External Validation

Author

Percy Soto Becerra

1 Setup

rm(list = ls())

# Use pacman to check whether packages are installed, if not load
if (!require("pacman")) install.packages("pacman")
library(pacman)

# Unload all package to begin in a session with only base packages
pacman::p_unload(all)

# Install packages
pacman::p_load(
  rio, 
  here, 
  tidyverse, 
  gtools, 
  kableExtra, 
  patchwork, 
  flextable, 
  furrr, 
  parallel, 
  mice, 
  survival,
  prodlim, 
  cmprsk,
  riskRegression,
  splines
)

source(here("Code", "source", "kfre_pi.R"))
source(here("Code", "source", "kfre_pr.R"))
source(here("Code", "source", "oe_ratio.R"))
source(here("Code", "source", "calibration_intercept.R"))
source(here("Code", "source", "calibration_slope.R"))
source(here("Code", "source", "auc.R"))
source(here("Code", "source", "auc_brier_boot.R"))
source(here("Code", "source", "validate.mids.R"))
source(here("Code", "source", "pool.validate.mids.R"))
source(here("Code", "source", "pool.auc.mids.R"))
source(here("Code", "source", "process_imp_cal_plot.R"))
source(here("Code", "source", "predict.mira.R"))
source(here("Code", "source", "performance_measures.R"))
source(here("Code", "source", "tidy_performance_stack.R"))    
source(here("Code", "source", "tidy_pool.R")) 
source(here("Code", "source", "process_imp_cal_plot2.R")) 

seed <- 2014

2 Load data

# # Import data
imp.datosA <- readRDS(here::here("Data", "Tidy", "Main-Winsorize-1_5", "data_impA.rds")) 
gc()
            used  (Mb) gc trigger   (Mb)  max used  (Mb)
Ncells   2832971 151.3    5252691  280.6   4101325 219.1
Vcells 117037097 893.0  151470922 1155.7 117048872 893.1

3 Configurate cores for parallel processing

n_cores <- detectCores()
n_cores <- (n_cores - 2) / 2
# Evaluate futures in parallel - max of two workers to avoid hogging resources
future::plan("multisession", workers = n_cores)

4 Pre-processing data

imp.datosA <- imp.datosA |> 
  mutate(risk2y = kfre_pr(imp.datosA, 2),
         risk5y = kfre_pr(imp.datosA, 5), 
         eventdf = factor(eventd)) |> 
  select(.imp, .id, time, eventd, eventdf, risk2y, risk5y) |>  
  filter(.imp != 0)

5 Predictive Performance

5.1 Calibration and Discrimination Measures

future::plan("multisession", workers = n_cores)
results_stack3a4_2y <- tidy_performance_stack(imp.datosA, 
                                  horizon = 2, 
                                  primary_event = 1, 
                                  pred = "risk2y",
                                  seed = seed, 
                                  n_cores = n_cores)

rio::export(results_stack3a4_2y , here("Data", "Tidy", "Main-Winsorize-1_5", 
                                       "res_valext__kfre_orig_stack3a4_2y.rds"))

future::plan("multisession", workers = n_cores)
results_stack3a4_5y <- tidy_performance_stack(imp.datosA, 
                                  horizon = 5, 
                                  primary_event = 1, 
                                  pred = "risk5y",
                                  seed = seed, 
                                  n_cores = n_cores)

rio::export(results_stack3a4_5y, here("Data", "Tidy", "Main-Winsorize-1_5", 
                                      "res_valext_kfre_orig_stack3a4_5y.rds"))
res_pool1 <- tidy_pool(results_stack3a4_2y) 

res_pool1 |> 
  kbl() |> 
  kable_classic(full_width = T, html_font = "Cambria")
term estimate ll ul pval ubar b t dfcom df riv lambda fmi n
Average predicted risk 0.0148486 NA NA NA NaN 0.0000001 NaN 30030 NA NaN NaN NaN 30031
Overall observerd risk 0.0273046 0.0254293 0.0291799 0.0000000 0.0000009 0.0000000 0.0000009 30030 30030.0000 0.0000000 0.0000000 0.0000666 30031
Log OE ratio 0.6092915 0.5329617 0.6856213 0.0000000 0.0012279 0.0002845 0.0015152 30030 2473.0857 0.2340161 0.1896378 0.0007311 30031
OE difference 0.0124560 0.0105161 0.0143959 0.0000000 0.0000009 0.0000001 0.0000010 30030 12686.3357 0.0699669 0.0653917 0.0001525 30031
Calibration Intercept 0.0248474 -0.1324316 0.1821265 0.7565925 0.0043575 0.0020444 0.0064224 30030 914.7292 0.4738640 0.3215113 0.0018290 30031
Calibration Slope 0.5824941 0.5329646 0.6320236 0.0000000 0.0005467 0.0000906 0.0006382 30029 4054.5128 0.1674280 0.1434161 0.0004576 30031
Logit AUC 1.9605067 1.8436399 2.0773735 0.0000000 0.0030191 0.0005287 0.0035531 30030 3740.4228 0.1768742 0.1502915 0.0004941 30031
Brier 0.0247911 0.0231400 0.0264421 0.0000000 0.0000007 0.0000000 0.0000007 30030 25245.4258 0.0239194 0.0233606 0.0000783 30031 
res_pool2 <- tidy_pool(results_stack3a4_5y) 

res_pool2 |> 
  kbl() |> 
  kable_classic(full_width = T, html_font = "Cambria")
term estimate ll ul pval ubar b t dfcom df riv lambda fmi n
Average predicted risk 0.0447519 NA NA NA NaN 0.0000005 NaN 30030 NA NaN NaN NaN 30031
Overall observerd risk 0.0476187 0.0450853 0.0501521 0.0000000 0.0000017 0.0000000 0.0000017 30030 30030.0000 0.0000000 0.0000000 0.0000666 30031
Log OE ratio 0.0622124 0.0007751 0.1236496 0.0471823 0.0007368 0.0002418 0.0009810 30030 1491.6060 0.3314888 0.2489610 0.0011716 30031
OE difference 0.0028668 -0.0000193 0.0057529 0.0515475 0.0000017 0.0000005 0.0000022 30030 1753.1433 0.2961194 0.2284662 0.0010088 30031
Calibration Intercept -0.4678735 -0.5889528 -0.3467942 0.0000000 0.0023383 0.0014492 0.0038020 30030 644.6382 0.6259778 0.3849854 0.0024937 30031
Calibration Slope 0.5801802 0.5423074 0.6180529 0.0000000 0.0003212 0.0000515 0.0003732 30029 4260.6666 0.1618482 0.1393024 0.0004364 30031
Logit AUC 1.7741859 1.6870515 1.8613202 0.0000000 0.0018599 0.0001150 0.0019761 30030 14229.1899 0.0624473 0.0587769 0.0001364 30031
Brier 0.0419170 0.0397886 0.0440455 0.0000000 0.0000011 0.0000001 0.0000012 30030 11823.2705 0.0746902 0.0694993 0.0001632 30031 
tab_res_2y <- res_pool1 |> 
  select(term, estimate, ll, ul) |> 
  mutate(
    across(c(estimate, ll, ul), ~ if_else(term == "Log OE ratio", exp(.x), .x)), 
    across(c(estimate, ll, ul), ~ if_else(term == "Logit AUC", exp(.x) / (1  + exp(.x)), .x)), 
    term = if_else(term == "Log OE ratio", "OE ratio", term), 
    term = if_else(term == "Logit AUC", "AUC", term), 
    across(c(estimate, ll, ul), ~ if_else(term %in% 
                                            c("Average predicted risk", 
                                              "Overall observerd risk", 
                                              "OE difference"), 100 * .x, .x)), 
    across(c(estimate, ll, ul), ~ round(.x, 2)), 
    measures = case_when(term == "Average predicted risk" ~ str_glue("{estimate}%"), 
                       term %in% c("Overall observerd risk", "OE difference") ~ str_glue("{estimate}% ({ll}% to {ul}%)"),
                       TRUE ~ str_glue("{estimate} ({ll} to {ul})")
                       )
    ) |> 
  select(term, measures) |> 
  mutate(grupo = c(rep("Calibration", 6), "Discrimination", "Overall performance"), 
         year = "2 years")

tab_res_5y <- res_pool2 |> 
  select(term, estimate, ll, ul) |> 
  mutate(
    across(c(estimate, ll, ul), ~ if_else(term == "Log OE ratio", exp(.x), .x)), 
    across(c(estimate, ll, ul), ~ if_else(term == "Logit AUC", exp(.x) / (1  + exp(.x)), .x)), 
    term = if_else(term == "Log OE ratio", "OE ratio", term), 
    term = if_else(term == "Logit AUC", "AUC", term), 
    across(c(estimate, ll, ul), ~ if_else(term %in% 
                                            c("Average predicted risk", 
                                              "Overall observerd risk", 
                                              "OE difference"), 100 * .x, .x)), 
    across(c(estimate, ll, ul), ~ round(.x, 2)), 
    measures = case_when(term == "Average predicted risk" ~ str_glue("{estimate}%"), 
                       term %in% c("Overall observerd risk", "OE difference") ~ str_glue("{estimate}% ({ll}% to {ul}%)"),
                       TRUE ~ str_glue("{estimate} ({ll} to {ul})")
                       )
    ) |> 
  select(term, measures) |> 
  mutate(grupo = c(rep("Calibration", 6), "Discrimination", "Overall performance"), 
         year = "5 years")

tab_res0 <- tab_res_2y |>
  bind_rows(tab_res_5y)

tab_res0 |> 
  as_grouped_data(groups = "year") |> 
  as_grouped_data(groups = "grupo") |> 
  flextable::as_flextable(hide_grouplabel = TRUE) |> 
  autofit() |> 
  set_header_labels(
    year = "Time horizon", 
    term = "Performance measure", 
    measures = "Original KFRE"
  ) |>  
  bold(j = 1) |> 
  set_caption("Table. Performance measures of KFRE in the external dataset of patients with CKD Stages 3a-4") |>  
  theme_booktabs() |>   
  bold(bold = TRUE, part = "header") -> table_perf_final

table_perf_final %>% 
  flextable::save_as_docx(path = here("Tables", "Main-Winsorize-1_5", "Table_Imputed_Performance_Modelo_Original.docx"))

table_perf_final

Time horizon

Performance measure

Original KFRE

2 years

Calibration

Average predicted risk

1.48%

Overall observerd risk

2.73% (2.54% to 2.92%)

OE ratio

1.84 (1.7 to 1.99)

OE difference

1.25% (1.05% to 1.44%)

Calibration Intercept

0.02 (-0.13 to 0.18)

Calibration Slope

0.58 (0.53 to 0.63)

Discrimination

AUC

0.88 (0.86 to 0.89)

Overall performance

Brier

0.02 (0.02 to 0.03)

5 years

Calibration

Average predicted risk

4.48%

Overall observerd risk

4.76% (4.51% to 5.02%)

OE ratio

1.06 (1 to 1.13)

OE difference

0.29% (0% to 0.58%)

Calibration Intercept

-0.47 (-0.59 to -0.35)

Calibration Slope

0.58 (0.54 to 0.62)

Discrimination

AUC

0.85 (0.84 to 0.87)

Overall performance

Brier

0.04 (0.04 to 0.04)

rm(list=ls()[! ls() %in% c("imp.datosA","vdata", "primary_event", "horizon", 
                           "process_imp_cal_plot", "seed", "n_cores")])
gc()
           used  (Mb) gc trigger  (Mb)  max used   (Mb)
Ncells  3177787 169.8    5252691 280.6   5252691  280.6
Vcells 24374928 186.0   93104695 710.4 181150158 1382.1

5.2 Moderate calibration: Calibration curves lowess based on subdistributional hazards

primary_event <- 1

n_internal_knots <- 5

# Seleccion del grupo: Stages 3-4----

# A 2 años----
horizon <- 2

vdata <- imp.datosA %>% 
  rename(pred = risk2y) |> 
  select(.imp, .id, time, eventd, pred) |> 
  mutate(cll_pred = log(-log(1 - pred)))

rcs_vdata <- ns(vdata$cll_pred, df = n_internal_knots + 1)
colnames(rcs_vdata) <- paste0("basisf_", colnames(rcs_vdata))
knots <- attr(rcs_vdata, "knots")
bound.knots <-  attr(rcs_vdata, "Boundary.knots")

pp <- seq(min(vdata$pred), max(vdata$pred), length.out = 1000)
cll_pp <- log(-log(1 - pp))
rcs_cll_pp <- ns(cll_pp, knots = knots, Boundary.knots = bound.knots)
colnames(rcs_cll_pp) <- paste0("basisf_", colnames(rcs_cll_pp))

vdata_bis_pp <- cbind(pp, as.data.frame(rcs_cll_pp))

future::plan("multisession", workers = n_cores)
subdist_df_imp <- future_map(1:max(vdata$.imp),
                         process_imp_cal_plot, 
                         vdata = vdata, 
                         primary_event = primary_event, 
                         horizon = horizon, 
                         type = "subdist_hazard", 
                         n_internal_knots = n_internal_knots, 
                         vdata_bis_pp, 
                         .options = furrr_options(seed = seed, 
                                                  packages = c("riskRegression", 
                                                               "survival", 
                                                               "splines", 
                                                               "cmprsk",
                                                               "tidyverse")), 
                         .progress = TRUE)
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[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
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[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
# 5 knots seems to give somewhat equivalent graph to pseudo method with bw = 0.05
subdist_df_imp_obs <- subdist_df_imp |> 
  bind_rows() |> 
  filter(type == "observed")

subdist_df_stack <- subdist_df_imp_obs |>
  group_by(.imp) |> 
  mutate(deciles_risk = as.integer(quantcut(risk, seq(0, 1, by = 0.1)))) |> 
  group_by(.imp, deciles_risk) |> 
  summarise(obs_mean_imp = mean(obs), 
            risk_mean_imp = mean(risk)) |> 
  group_by(deciles_risk) |> 
  summarise(obs_mean_pool = mean(obs_mean_imp), 
            risk_mean_pool = mean(risk_mean_imp))
  
subdist_df_imp_fix <- subdist_df_imp |> 
  bind_rows() |>  
  filter(type == "fixed") |> 
  arrange(risk) |> 
  summarise(obs_pool = mean(obs), 
            .by = risk) |> 
  mutate(deciles_risk = quantcut(risk, seq(0, 1, by = 0.1)))

rio::export(subdist_df_imp, here("Data", "Tidy", "Main-Winsorize-1_5", "subdist_df_imput_3a4_2y.rds"))
rio::export(subdist_df_stack, here("Data", "Tidy", "Main-Winsorize-1_5", "subdist_df_deciles_3a4_2y.rds"))

cal_mod2y_imp <- subdist_df_imp_obs |> 
  select(.imp, risk, obs) |> 
  summarise(ICI = mean(abs(risk - obs)), 
            E50 = quantile(abs(risk - obs), c(0.5)), 
            E90 = quantile(abs(risk - obs), c(0.9)), 
            Emax = max(abs(risk - obs)), 
            root_square_bias = sqrt(mean((risk - obs) ^ 2)), 
            .by = ".imp"
  ) 

cal_mod2y_pool <- cal_mod2y_imp |> 
  summarise(ICI = mean(ICI), 
            E50 = mean(E50), 
            E90 = mean(E90), 
            Emax = mean(Emax), 
            root_square_bias = mean(root_square_bias)) |> 
  mutate(year = "2 years") |> 
  select(year, everything())

rio::export(cal_mod2y_imp, here("Data", "Tidy", "Main-Winsorize-1_5", "cal_Original2y_imp.rds"))

# Grafico de calibracion
ggplot() +
  geom_abline(intercept = 0, slope = 1, colour = "red", linetype = 2) + 
  geom_line(data = subdist_df_imp_fix, 
            aes(x = risk, y = obs_pool),
            alpha = 0.5, color = "black") +
  geom_point(data = subdist_df_stack,
             aes(x = risk_mean_pool, y = obs_mean_pool),
             shape = 23,
             stroke = 0.1,
             fill = "blue") + 
  scale_y_continuous(breaks = seq(0, 1, 0.2), limits = c(0, 1)) +
  scale_x_continuous(breaks = seq(0, 1, 0.2), limits = c(0, 1)) +
  theme_bw() + 
  labs(x = "Predicted risks", y = "Observed outcome proportions") + 
  # geom_rug(data = subdist_df_stack,
  #          aes(x = risk_mean_pool, y = obs_mean_pool),
  #          alpha = 0.1) +
  coord_fixed(ratio = 1, expand = TRUE)  -> plot_mod0_2y

# Grafico de calibracion con curvas imputadas
plot_mod0_2y + 
  geom_line(data = subdist_df_imp_obs, 
            aes(x = risk, y = obs, group = .imp),
            alpha = 0.1, color = "#38B8F7") -> plot_mod0_imp_2y

# A 5 años----
horizon <- 5

vdata <- imp.datosA %>% 
  rename(pred = risk5y) |> 
  select(.imp, .id, time, eventd, pred) |> 
  mutate(cll_pred = log(-log(1 - pred))) 

rcs_vdata <- ns(vdata$cll_pred, df = n_internal_knots + 1)
colnames(rcs_vdata) <- paste0("basisf_", colnames(rcs_vdata))
knots <- attr(rcs_vdata, "knots")
bound.knots <-  attr(rcs_vdata, "Boundary.knots")

pp <- seq(min(vdata$pred), max(vdata$pred), length.out = 1000)
cll_pp <- log(-log(1 - pp))
rcs_cll_pp <- ns(cll_pp, knots = knots, Boundary.knots = bound.knots)
colnames(rcs_cll_pp) <- paste0("basisf_", colnames(rcs_cll_pp))

vdata_bis_pp <- cbind(pp, as.data.frame(rcs_cll_pp))

future::plan("multisession", workers = n_cores)
subdist_df_imp <- future_map(1:max(vdata$.imp),
                         process_imp_cal_plot, 
                         vdata = vdata, 
                         primary_event = primary_event, 
                         horizon = horizon, 
                         type = "subdist_hazard", 
                         n_internal_knots = n_internal_knots, 
                         vdata_bis_pp, 
                         .options = furrr_options(seed = seed, 
                                                  packages = c("riskRegression", 
                                                               "survival", 
                                                               "splines", 
                                                               "cmprsk",
                                                               "tidyverse")), 
                         .progress = TRUE)
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
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[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
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[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
[1] "basisf_1" "basisf_2" "basisf_3" "basisf_4" "basisf_5" "basisf_6"
# 5 knots seems to give somewhat equivalent graph to pseudo method with bw = 0.05
subdist_df_imp_obs <- subdist_df_imp |> 
  bind_rows() |> 
  filter(type == "observed")

subdist_df_stack <- subdist_df_imp_obs |>
  group_by(.imp) |> 
  mutate(deciles_risk = as.integer(quantcut(risk, seq(0, 1, by = 0.1)))) |> 
  group_by(.imp, deciles_risk) |> 
  summarise(obs_mean_imp = mean(obs), 
            risk_mean_imp = mean(risk)) |> 
  group_by(deciles_risk) |> 
  summarise(obs_mean_pool = mean(obs_mean_imp), 
            risk_mean_pool = mean(risk_mean_imp))
  
subdist_df_imp_fix <- subdist_df_imp |> 
  bind_rows() |>  
  filter(type == "fixed") |> 
  arrange(risk) |> 
  summarise(obs_pool = mean(obs), 
            .by = risk) |> 
  mutate(deciles_risk = quantcut(risk, seq(0, 1, by = 0.1)))

rio::export(subdist_df_imp, here("Data", "Tidy", "Main-Winsorize-1_5", "subdist_df_imput_3a4_5y.rds"))
rio::export(subdist_df_stack, here("Data", "Tidy", "Main-Winsorize-1_5", "subdist_df_deciles_3a4_5y.rds"))

cal_mod5y_imp <- subdist_df_imp_obs |> 
  select(.imp, risk, obs) |> 
  summarise(ICI = mean(abs(risk - obs)), 
            E50 = quantile(abs(risk - obs), c(0.5)), 
            E90 = quantile(abs(risk - obs), c(0.9)), 
            Emax = max(abs(risk - obs)), 
            root_square_bias = sqrt(mean((risk - obs) ^ 2)), 
            .by = ".imp"
  ) 

cal_mod5y_pool <- cal_mod5y_imp |> 
  summarise(ICI = mean(ICI), 
            E50 = mean(E50), 
            E90 = mean(E90), 
            Emax = mean(Emax), 
            root_square_bias = mean(root_square_bias)) |> 
  mutate(year = "5 years") |> 
  select(year, everything())

rio::export(cal_mod5y_imp, here("Data", "Tidy", "Main-Winsorize-1_5", "cal_Original5y_imp.rds"))
# Grafico de calibracion
ggplot() +
  geom_abline(intercept = 0, slope = 1, colour = "red", linetype = 2) + 
  geom_line(data = subdist_df_imp_fix, 
            aes(x = risk, y = obs_pool),
            alpha = 0.5, color = "black") +
  geom_point(data = subdist_df_stack,
             aes(x = risk_mean_pool, y = obs_mean_pool),
             shape = 23,
             stroke = 0.1,
             fill = "blue", 
             alpha = 0.5) + 
  scale_y_continuous(breaks = seq(0, 1, 0.2), limits = c(0, 1)) +
  scale_x_continuous(breaks = seq(0, 1, 0.2), limits = c(0, 1)) +
  theme_bw() + 
  labs(x = "Predicted risks", y = "Observed outcome proportions") + 
  # geom_rug(data = subdist_df_stack,
  #          aes(x = risk_mean_pool, y = obs_mean_pool),
  #          alpha = 0.1) +
  coord_fixed(ratio = 1, expand = TRUE)  -> plot_mod0_5y

# Grafico de calibracion con curvas imputadas
plot_mod0_5y + 
  geom_line(data = subdist_df_imp_obs, 
            aes(x = risk, y = obs, group = .imp),
            alpha = 0.3, color = "#38B8F7") -> plot_mod0_imp_5y

## Grafico final
plot_mod0_2y <- plot_mod0_2y + 
  labs(title = "Original Model\n(2 year KFRE)") + 
  theme(plot.title = element_text(hjust = 0.5))

plot_mod0_5y <- plot_mod0_5y + 
  labs(title = "Original Model\n(5 year KFRE)") + 
  theme(plot.title = element_text(hjust = 0.5))

plot_mod0_imp_2y <- plot_mod0_imp_2y +
  labs(title = "Original Model\n(2 year KFRE)") +
  theme(plot.title = element_text(hjust = 0.5))

plot_mod0_imp_5y <- plot_mod0_imp_5y +
  labs(title = "Original Model\n(5 year KFRE)") +
  theme(plot.title = element_text(hjust = 0.5))

plot_cal_mod0 <- (plot_mod0_2y | plot_mod0_5y) + plot_annotation(tag_levels = "a")
plot_cal_imp_mod0 <- (plot_mod0_imp_2y | plot_mod0_imp_5y) + plot_annotation(tag_levels = "a")

export(plot_mod0_2y, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_mod0_2y.rds"))
export(plot_mod0_5y, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_mod0_5y.rds"))
export(plot_cal_mod0, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_cal_mod0.rds"))

export(plot_mod0_imp_2y, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_mod0_imp_2y.rds"))
export(plot_mod0_imp_5y, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_mod0_imp_5y.rds"))
export(plot_cal_imp_mod0, here("Data", "Tidy", "Main-Winsorize-1_5", "plot_cal_imp_mod0.rds"))


ggsave(filename = "Plot_Calibration_imputed.jpeg", 
       device = "jpeg", 
       plot = plot_cal_mod0, 
       path = here("Figures", "Main-Winsorize-1_5"), 
       scale = 2, 
       width = 12, 
       height = 6,
       units = "cm", 
       dpi = 1000)

ggsave(filename = "Plot_Calibration_imputed_estabilidad.jpeg", 
       device = "jpeg", 
       plot = plot_cal_imp_mod0, 
       path = here("Figures", "Main-Winsorize-1_5"), 
       scale = 2, 
       width = 12, 
       height = 6,
       units = "cm", 
       dpi = 1000)

gc()
           used  (Mb) gc trigger   (Mb)  max used   (Mb)
Ncells  3343159 178.6    5252691  280.6   5252691  280.6
Vcells 85954162 655.8  272778960 2081.2 272766285 2081.1
knitr::include_graphics(here("Figures", "Main-Winsorize-1_5", "Plot_Calibration_imputed.jpeg"))

Calibration curves for each group and prediction horizon
knitr::include_graphics(here("Figures", "Main-Winsorize-1_5", "Plot_Calibration_imputed_estabilidad.jpeg"))

Calibration curves for each group and prediction horizon

5.3 Moderate Calibration

cal_mod2y_pool |> 
  bind_rows(cal_mod5y_pool) |> 
  pivot_longer(cols = ICI:root_square_bias, 
               names_to = "metrica", 
               values_to = "modelo") |> 
  mutate(modelo = round(modelo, 3)) |> 
  as_grouped_data(groups = "year") |> 
  flextable::as_flextable(hide_grouplabel = TRUE) |> 
  autofit() |>  
  set_header_labels(
    year = "Time horizon", 
    metrica = "Performance measure", 
    modelo = "Original KFRE"
  ) |> 
  bold(i = c(1, 7), j = 1) |> 
  set_caption("Table. Moderate Calibration Metrics") |>  
  theme_booktabs() |>   
  bold(bold = TRUE, part = "header") -> table_cal_mod

table_cal_mod %>% 
  flextable::save_as_docx(path = here("Tables", "Main-Winsorize-1_5", "Table_Imputed_Performance_Moderate_Cal_Modelo_Original.docx"))

table_cal_mod

Performance measure

Original KFRE

2 years

ICI

0.016

E50

0.005

E90

0.049

Emax

0.541

root_square_bias

0.031

5 years

ICI

0.017

E50

0.005

E90

0.035

Emax

0.475

root_square_bias

0.049

6 Reproducibility Ticket

sessionInfo()
R version 4.4.1 (2024-06-14)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.12.0 
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0

Random number generation:
 RNG:     L'Ecuyer-CMRG 
 Normal:  Inversion 
 Sample:  Rejection 
 
locale:
 [1] LC_CTYPE=es_ES.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=es_ES.UTF-8        LC_COLLATE=es_ES.UTF-8    
 [5] LC_MONETARY=es_ES.UTF-8    LC_MESSAGES=es_ES.UTF-8   
 [7] LC_PAPER=es_ES.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=es_ES.UTF-8 LC_IDENTIFICATION=C       

time zone: America/Lima
tzcode source: system (glibc)

attached base packages:
[1] splines   parallel  stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] riskRegression_2023.12.21 cmprsk_2.2-12            
 [3] prodlim_2024.06.25        survival_3.7-0           
 [5] mice_3.16.0               furrr_0.3.1              
 [7] future_1.34.0             flextable_0.9.6          
 [9] patchwork_1.2.0           kableExtra_1.4.0         
[11] gtools_3.9.5              lubridate_1.9.3          
[13] forcats_1.0.0             stringr_1.5.1            
[15] dplyr_1.1.4               purrr_1.0.2              
[17] readr_2.1.5               tidyr_1.3.1              
[19] tibble_3.2.1              ggplot2_3.5.1            
[21] tidyverse_2.0.0           here_1.0.1               
[23] rio_1.2.2                

loaded via a namespace (and not attached):
  [1] rstudioapi_0.16.0       jsonlite_1.8.8          shape_1.4.6.1          
  [4] magrittr_2.0.3          TH.data_1.1-2           jomo_2.7-6             
  [7] farver_2.1.2            nloptr_2.1.1            rmarkdown_2.28         
 [10] geepack_1.3.11          ragg_1.3.2              vctrs_0.6.5            
 [13] minqa_1.2.8             askpass_1.2.0           base64enc_0.1-3        
 [16] htmltools_0.5.8.1       polspline_1.1.25        broom_1.0.6            
 [19] Formula_1.2-5           mitml_0.4-5             parallelly_1.38.0      
 [22] htmlwidgets_1.6.4       sandwich_3.1-0          zoo_1.8-12             
 [25] uuid_1.2-1              lifecycle_1.0.4         iterators_1.0.14       
 [28] pkgconfig_2.0.3         Matrix_1.7-0            R6_2.5.1               
 [31] fastmap_1.2.0           digest_0.6.37           numDeriv_2016.8-1.1    
 [34] colorspace_2.1-1        rprojroot_2.0.4         textshaping_0.4.0      
 [37] Hmisc_5.1-3             fansi_1.0.6             timechange_0.3.0       
 [40] compiler_4.4.1          fontquiver_0.2.1        withr_3.0.1            
 [43] htmlTable_2.4.3         backports_1.5.0         highr_0.11             
 [46] R.utils_2.12.3          pan_1.9                 MASS_7.3-61            
 [49] lava_1.8.0              quantreg_5.98           openssl_2.2.1          
 [52] tools_4.4.1             foreign_0.8-86          zip_2.3.1              
 [55] future.apply_1.11.2     nnet_7.3-19             R.oo_1.26.0            
 [58] glue_1.7.0              mets_1.3.4              nlme_3.1-165           
 [61] grid_4.4.1              checkmate_2.3.2         cluster_2.1.6          
 [64] generics_0.1.3          gtable_0.3.5            tzdb_0.4.0             
 [67] R.methodsS3_1.8.2       data.table_1.16.0       hms_1.1.3              
 [70] xml2_1.3.6              utf8_1.2.4              foreach_1.5.2          
 [73] pillar_1.9.0            lattice_0.22-5          SparseM_1.84-2         
 [76] tidyselect_1.2.1        fontLiberation_0.1.0    rms_6.8-2              
 [79] knitr_1.48              fontBitstreamVera_0.1.1 gridExtra_2.3          
 [82] svglite_2.1.3           xfun_0.47               stringi_1.8.4          
 [85] yaml_2.3.10             pacman_0.5.1            boot_1.3-30            
 [88] evaluate_0.24.0         codetools_0.2-20        officer_0.6.6          
 [91] gdtools_0.4.0           cli_3.6.3               rpart_4.1.23           
 [94] systemfonts_1.1.0       munsell_0.5.1           Rcpp_1.0.13            
 [97] globals_0.16.3          MatrixModels_0.5-3      jpeg_0.1-10            
[100] lme4_1.1-35.5           listenv_0.9.1           glmnet_4.1-8           
[103] viridisLite_0.4.2       mvtnorm_1.3-1           timereg_2.0.6          
[106] scales_1.3.0            rlang_1.1.4             multcomp_1.4-26